A startling red box has landed on the South Bank, nestled near the National Theatre right by Waterloo bridge. This is the Shed, by Haworth Tompkins architects, a temporary auditorium for the NT while its Cottesloe (now Dorfman) Theatre undergoes a year-long refurbishment. With four proud chimneys and rough red-stained boarding, it recalls a diminutive Battersea Power Station as if built by Amish barn-raisers.

"We wanted something festive, which would contrast with the brutalist concrete mass of Denys Lasdun's building," says architect Paddy Dillon. "But it should also feel like part of the existing complex." Coming over the bridge, the bright red Shed is an arresting sight, half packing crate, half temple – but it seems a natural addition to Lasdun's National, all bulky chiselled forms. Its chimneys rhyme with the verticals of the theatre's lift shafts, while its cubic mass echoes the monolithic fly-tower behind – as if it had leapt to the ground and daubed itself with face paint to join in some South Bank fun.

The Shed's influences have an appropriately theatrical air: from the red oxide boarding of rural Swedish houses to the 1973 Clint Eastwood film High Planes Drifter, in which the Stranger paints an entire town red and rides off into the sunset. Its makeshift aesthetic is also in tune with the South Bank's palette-clad container restaurants and other temporary flotsam that comes and goes with the riverside's festivals of fun, although this has a noticeably higher quality – plus a £1.2m price tag.

The rough-sawn timber has been carefully sized to match the board-marking on Lasdun's concrete, while the entire thing is lined with acoustically insulating cassettes and naturally ventilated by the chimney stacks: "It's not just a tent," says Dillon. The building occupies the sunken terrace known as Theatre Square, in front of the National's coffee bar, and cleverly stitches itself into the existing structure. A new polycarbonate screen encloses part of the terrace, forming a temporary foyer for the Shed, which is fitted out internally with rough-and-ready plywood furniture and eclectic finds from the prop store.

The Shed nestles in the embrace of the National Theatre's concrete flanks. Photograph: Philip Vile PR

Inside, the 250-seat theatre is more than a simple black box, with a formal octagonal seating setup (using seats recycled from the Cottesloe) and the raw steel frame left exposed, subtle blooms of rust adding a warm tinge. Basic scaffolding balustrades and cord netting, simple bulkhead lamps and festooned builder's lights add to the provisional construction-site aesthetic – in line with the more experimental productions the space will be hosting.

Haworth Tompkins is a practice well-versed in the ways of the stage, having magically reworked the Royal Court and Young Vic, as well as building two temporary theatres for the Almeida and being involved in an ongoing programme of tweaks to the Battersea Arts Centre. Like its work at the BAC, the Shed is the result of their increasing desire to operate more like theatres do themselves.

"There is a huge gulf between the weighty, ponderous way that buildings are made and the way the theatre works," says Dillon. "We're trying to learn from the quicker, more agile manner in which the National puts on its shows. The Shed was developed more as an event than a building."

The project came out of the practice's long-term £70m NT Future masterplan, which includes a new production building, remodelled workshops and extensive interior restoration, as well as a bid to improve the theatre's relationship with the riverfront. But while the Shed is essentially a byproduct of permanent works, it points to an alternative model for how the South Bank's unwieldy structures can be adapted with light-footed architecture. Unlike the proposed plans for the Southbank Centre next door – which will likely see great glass boxes strapped to the roof and the side of the complex, and the entire undercroft packed with shops and restaurants – the Shed transforms part of this rambling concrete landscape without being fixed in time. It is a model of nimble intervention that its neighbours would do well to learn from.